Exponentiated power Lindley power series class of distributions: Theory and applications

M. Alizadeh, S. F. Bagheri, E. Bahrami Samani, S. Ghobadi, S. Nadarajah

    Research output: Contribution to journalArticlepeer-review


    We introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley power series (EPLPS) distribution. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the minimum lifetime value among all risks. The distribution exhibits a variety of bathtub-shaped hazard rate functions. It contains as particular cases several lifetime distributions. Various properties of the distribution are investigated including closed-form expressions for the density function, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Expressions for the Rényi and Shannon entropies are also given. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Finally, two data applications are given showing flexibility and potentiality of the EPLPS distribution.

    Original languageEnglish
    Pages (from-to)1-33
    Number of pages33
    JournalCommunications in Statistics: Simulation and Computation
    Early online date6 Jul 2017
    Publication statusPublished - 2017


    • Hazard rate function
    • Maximum likelihood estimation
    • Model selection criteria
    • Power series distributions
    • Residual life function.


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